Integration of Optimization Algorithms With Sensitivity Analysis, With Application to Volcanic Regions

Language:

English

Abstract:

The purpose of this thesis is the generation of improved optimization approaches, applied to a volcanic modeling. Neither local nor global optimization algorithms can guarantee the generation of a global optimization solution. Furthermore, the generated models have to be integrated into the physical context of other available observations and models in the specific volcanic region. A reliable optimization result can only be given by a model with significant determined parameters which can be seen on small dispersion if the optimization is carried out several times as well as considering the results of statistical tests about the model fit. In addition, this model has to be validated by additional information from other observation techniques and models. Different improvements of the optimization have been analyzed within this thesis: (1) The first approach is given by the definition of physical constraints, which are implemented into the optimization approach by penalty terms. This approach shall lead to a decrease of possible solutions so the dispersion of the unknown parameters is decreased, which is equal to an increase of significance of these unknown parameters. (2) Another approach of improvement is given by the implementation of the results from a global sensitivity analysis. A re-weighting factor is implemented into the optimization approach, so the weight of the observations is varied with respect to their sensitivity against changes in a specific unknown parameter. (3) The last improvement approach is described by the implementation of a fuzzy logic model. This model fuses physical plausibility checks as well as available density data of the volcanic region. The fuzzy logic model results in a physical reliability value for the model. This approach is implemented actively into the optimization approach by an addend to the objective function. The generated models without any implementation improvements serve as reference. Data collected at the high risk volcano Merapi at Central Java, Indonesia serve as a case study. The modeling is based on a non-linear inversion of gravity changes and three-dimensional displacements which were measured between the years 2000 and 2002 at Merapi. The physical based mathematical model is described by the generalized static Navier equations which are solved for the mathematical half-space where elastic and gravitational effects are coupled. The parameters which have to be determined are given by the point mass of source, its position, and an energy value, described by the product of pressure and cubed radius. The different improvement approaches have been implemented into two different optimization algorithms: A downhill simplex and a genetic algorithm. The best optimization approach has been determined by comparing the different optimization configurations. The comparison results in the definition of a recommended optimization approach concerning the model's significance and physical reliability. The approach given by the implementation of the sensitivity analysis results into the genetic algorithm could determine the best elastic-gravitational source model concerning the dispersion of the unknown parameters and the fitness value of the result. Finally, the application of the fuzzy logic is used to validate these results with respect to the physical reliability of the elastic-gravitational source's position. So the quality of the model can be described statistically as well as physically. Nevertheless, all optimization configurations showed that a model which is solely based on a magmatic source is not feasible. All optimization results showed very shallow sources with small mass components and large energy values. These properties as well as the lack of ability to model the deformations lead to the assumption that another influence is acting. This effect is modelled by superposition of a local fault zone to the assumed magmatic source. This final model results in statistical significant and physical reliable parameters for a volcanic source superimposed with the effects of a fault zone. The model is statistically significant with a larger significance level than the models which are based on a solely elastic-gravitational source. In addition, this combined model also fits into the prior anticipations about the structure of Merapi given in the literature.